Why the two schedules clash less than you'd think
A hamster's day starts roughly when your child's ends. Hamsters wake at dusk, run, forage and rearrange their bedding through the small hours, then burrow down and sleep solidly through daylight — which is exactly when your child is at school and the bedroom sits empty. The overlap problem is narrower than it first looks: the first hour after lights-out, when the hamster is warming up and your child is drifting off, and any night noise that carries across a small room. Solve those two things and the arrangement is not a compromise at all; the hamster gets a quiet, dark room all day, which is precisely what he would choose.
Set the cage up for quiet nights
The wheel is the make-or-break purchase. Cheap wheels rattle against their stands and squeak at the axle, and a hamster can run for hours at full tilt. A solid-surface silent spinner, sized so his back stays flat while he runs, removes nearly all of it. Put the cage on the opposite side of the room from the bed, ideally on a stand or mat that absorbs vibration rather than a bare wooden floor that carries every knock. Bar-chewing is the other night noise to plan for: it usually means the cage is too small or too empty, so give him depth of bedding to dig in, a house to sleep in through the day, and things to shred, and the chewing mostly turns into quieter work. In the evening, dim the room rather than blazing the main light over the cage until bedtime — hamsters read bright light as daytime and will delay waking, which pushes their noisy peak later into your child's sleep.
Build the shared hour into the early evening
The part a child actually wants — watching him pouch food, holding him, the playpen on the floor — belongs in the early evening, before the bedtime routine starts. That window suits the hamster too: he is freshly awake and hungry rather than groggy. Make it a fixed fixture, the way story time is, so the hamster's handling ends when teeth-brushing begins and nobody is bargaining to get him out again at nine o'clock. Resist daytime wake-ups entirely. A hamster hauled out at lunchtime on a weekend is a stressed, nippy hamster, and broken daytime sleep is what turns a placid pet into a grumpy one; if your child wants to check on him in daylight, peeking at the sleeping house without opening it is the house rule.
What to watch for as they settle in
Give the arrangement a couple of weeks before judging it. If your child is waking repeatedly, listen for the specific sound — a gnawed cage bar, a water bottle clinking, the wheel stand rocking — because each one has its own fix, from repositioning the bottle to a heavier wheel base. If the hamster starts sleeping in odd corners or seems frantic the moment he wakes, he may be getting disturbed in the day; a small sign on the bedroom door during school holidays fixes most of that. KinsLe's Family Sharing keeps the hamster's routine — feeding times, cleaning day, the no-daytime-waking rule — written on one shared profile, so parents, the child and any grandparent on duty are all working from the same plan rather than improvising around a sleeping hamster.